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University Physics Volume 3

17th Edition
William Moebs + 1 other
ISBN: 9781938168185
BuyFindarrow_forward

University Physics Volume 3

17th Edition
William Moebs + 1 other
ISBN: 9781938168185
Textbook Problem

Using the solution from the previous problem, find the increase in rotational kinetic energy, given the core’s mass is 1.3 times that of out Sun. Where does this increase in kinetic energy come from?

To determine

The increase in rotational kinetic energy when star collapses.

Explanation

Given:

Mass of the core is 1.3 times of the Sun.

Formula used:

Rotational kinetic energy is calculated by

  KE=12Iω2

Calculation:

The moment of inertia is, I=25Mr2

The kinetic energy of the star is given as

  KE=12Iω2KE=12(25Mr2)ω2KE=15Mr2ω2=15Mr2(2πv)2

The initial kinetic energy of the star which is before it collapsed, is calculated as follows,

Substitute 5×105km for r 1.3×1.99×1030kg for M and 1259000s for v.

  KE=15Mr2(2πv)2KE=(0.2)(1.3)(1.99× 10 30kg)(5× 10 8m)2(2π)2(3.858× 10 7 s 1)2KE=7

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